General Information

Aim

Practical and theoretical knowledge in modelling, estimation,
validation, prediction, and interpolation of time discrete
dynamical stochastic systems, mainly linear systems. The course
also gives a basis for further studies of time series systems, e.g.
Financial statistics and Non-linear systems.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

be able to construct a model based on data for a concrete
practical time series problem,

be able to perform simple transformations of a non-stationary
time series into a stationary time series,

be able to predict and interpolate in linear time series
models,

be able to estimate parameters in linear time series models and
validate a resulting model,

be able to construct a Kalman-filter based on a linear state
model,

be able to estimate in time varying stochastic systems using
recursive and adaptive techniques.

Competences and skills
For a passing grade the student must

be able to present the analysis of a practical problem in a
written report and present it orally.

Contents

Time series analysis concerns the mathematical modelling of time
varying phenomena, e.g., ocean waves, water levels in lakes and
rivers, demand for electrical power, radar signals, muscular
reactions, ECG-signals, or option prices at the stock market. The
structure of the model is chosen both with regard to the physical
knowledge of the process, as well as using observed data. Central
problems are the properties of different models and their
prediction ability, estimation of the model parameters, and the
model's ability to accurately describe the data. Consideration must
be given to both the need for fast calculations and to the presence
of measurement errors. The course gives a comprehensive
presentation of stochastic models and methods in time series
analysis. Time series problems appear in many subjects and
knowledge from the course is used in, i.a., automatic control,
signal processing, and econometrics.

Further studies of ARMA-processes. Non-stationary models, slowly
decreasing dependence. Transformations. Optimal prediction and
reconstruction of processes. State representation, principle of
orthogonality, and Kalman filtering. Parameter estimation: Least
squares and Maximum likelihood methods as well as recursive and
adaptive variants. Non-parametric methods,covariance estimation,
spectral estimation. An orientation on robust methods and detection
of outliers.

Examination details

Grading scale: THAssessment: Written and oral project presentation with home exam, and compulsory computer exercises. The final grade is based on the project and the take-home exam.